*31.Express 5.31 centimeters in meters, millimeters, kilome-
ters, and micrometers.
*32.Express (a) 1.00 ft^3 in liters; (b) 1.00 L in pints; (c) miles
per gallon in kilometers per liter.
*33.The screen of a laptop computer measures 8.25 in. wide
and 6.25 in. tall. If this computer were being sold in
Europe, what would be the metric size of the screen used
in the specifications for the computer?
*34.If the price of gasoline is $1.229/gal, what is its price in
cents per liter?
*35.Suppose your automobile gas tank holds 16 gal and the
price of gasoline is $0.325/L. How much would it cost to
fill your gas tank?
*36.What is the density of silicon, if 50.6 g occupies 21.72 mL?
*37.What is the mass of a rectangular piece of copper
24.4 cm11.4 cm7.9 cm? The density of copper is
8.92 g/cm^3.
*38.A small crystal of sucrose (table sugar) had a mass of
5.536 mg. The dimensions of the box-like crystal were
2.20 mm1.36 mm1.12 mm. What is the density of
sucrose expressed in g/cm^3?
*39.Vinegar has a density of 1.0056 g/cm^3. What is the mass
of three L of vinegar?
*40.The density of silver is 10.5 g/cm^3. (a) What is the
volume, in cm^3 , of an ingot of silver with mass 0.615 kg?
(b) If this sample of silver is a cube, how long is each edge
in cm? (c) How long is the edge of this cube in inches?
*41.A container has a mass of 73.91 g when empty and
91.44 g when filled with water. The density of water is
1.0000 g/cm^3. (a) Calculate the volume of the container.
(b) When filled with an unknown liquid, the container had
a mass of 88.42 g. Calculate the density of the unknown
liquid.
*42.The mass of an empty container is 77.664 g. The mass of
the container filled with water is 99.646 g. (a) Calculate
the volume of the container, using a density of 1.0000
g/cm^3 for water. (b) A piece of metal was added to the
empty container, and the combined mass was 85.308 g.
Calculate the mass of the metal. (c) The container with the
metal was filled with water, and the mass of the entire sys-
tem was 106.442 g. What mass of water was added?
(d) What volume of water was added? (e) What is the vol-
ume of the piece of metal? (f ) Calculate the density of the
metal.
*43.A solution is 40.0% acetic acid (the characteristic compo-
nent in vinegar) by mass. The density of this solution is
1.049 g/mL at 20°C. Calculate the mass of pure acetic acid
in 100.0 mL of this solution at 20°C.Heat Transfer and Temperature Measurement
*44.Which represents a larger temperature interval: (a) a
Celsius degree or a Fahrenheit degree? (b) a kelvin or a
Fahrenheit degree?*45.Express (a) 283°C in K; (b) 15.25 K in °C; (c) 32.0°C in
°F; (d) 100.0°F in K.
*46.Express (a) 0°F in °C; (b) 98.6°F in K; (c) 298 K in °F;
(d) 11.3°C in °F.
*47.Make each of the following temperature conversions:
(a) 27°C to °F, (b) 27°C to °F, and (c) 100°F to °C.
*48.On the Réamur scale, which is no longer used, water
freezes at 0°R and boils at 80°R. (a) Derive an equation
that relates this to the Celsius scale. (b) Derive an equa-
tion that relates this to the Fahrenheit scale. (c) Mercury
is a liquid metal at room temperature. It boils at 356.6°C
(673.9°F). What is the boiling point of mercury on the
Réamur scale?
*49.Liquefied gases have boiling points well below room tem-
perature. On the Kelvin scale the boiling points of the fol-
lowing gases are: He, 4.2 K; N 2 , 77.4 K. Convert these
temperatures to the Celsius and the Fahrenheit scales.
*50.Convert the temperatures at which the following metals
melt to the Celsius and Fahrenheit scales: Al, 933.6 K; Ag,
1235.1 K.
*51.What is the melting point of lead in °F (mp327.5°C)?
*52.The average temperature of a healthy German shepherd is
101.5°F. Express this temperature in degrees Celsius.
Express this temperature in kelvins.
*53.Calculate the amount of heat required to raise the tem-
perature of 78.2 g of water from 10.0°C to 35.0°C. The
specific heat of water is 4.18 J/g°C.
*54.The specific heat of aluminum is 0.895 J/g°C. Calculate
the amount of heat required to raise the temperature of
22.1 g of aluminum from 27.0°C to 65.5°C.
*55.How much heat must be removed from 15.5 g of water at
90.0°C to cool it to 43.2°C?
*56.In some solar-heated homes, heat from the sun is stored
in rocks during the day and then released during the cooler
night. (a) Calculate the amount of heat required to raise
the temperature of 78.7 kg of rocks from 25.0°C to 43.0°C.
Assume that the rocks are limestone, which is essentially
pure calcium carbonate. The specific heat of calcium car-
bonate is 0.818 J/g°C. (b) Suppose that when the rocks in
part (a) cool to 30.0°C, all the heat released goes to warm
the 10,000 ft^3 (2.83 105 L) of air in the house, originally
at 10.0°C. To what final temperature would the air be
heated? The specific heat of air is 1.004 J/g°C, and its
density is 1.20 10 ^3 g/mL.
*57.A small immersion heater is used to heat water for a cup
of coffee. We wish to use it to heat 235 mL of water (about
a teacupful) from 25°C to 90°C in 2.00 min. What must
be the heat rating of the heater, in kJ/min, to accomplish
this? Ignore the heat that goes to heat the cup itself. The
density of water is 0.997 g/mL.
*58.When 75.0 grams of metal at 75.0°C is added to 150 grams
of water at 15.0°C, the temperature of the water rises to
18.3°C. Assume that no heat is lost to the surroundings.
What is the specific heat of the metal?Exercises 43